Sauté onion in butter; set aside.
 In a medium saucepan, over medium heat, cook melted butter and flour, using a whisk, for 3 - 5 minutes. 
 Stir constantly and add the half and half.
 Add the chicken stock; simmer for 20 minutes.
 Add the broccoli, carrots and onions. 
 Cook, over low heat, for 20 - 25 minutes.
 Add salt and pepper, to taste. 
 Can be puréed in a blender but serving without blending is also very good. 
 After blending, return to heat and add cheese. 
 Stir in nutmeg.